Chaotic Merge

You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s.

Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order.

A merge z is produced from a sequence a by the following rules:

• if a_i=0, then remove a letter from the beginning of x and append it to the end of z;
• if a_i=1, then remove a letter from the beginning of y and append it to the end of z.

Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i.

Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i.

Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive.

Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered.

Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353.

Input

The first line contains a string x (1 ≤ |x| ≤ 1000).

The second line contains a string y (1 ≤ |y| ≤ 1000).

Both strings consist only of lowercase Latin letters.

Output

Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353.

Examples

Input

aaa bb

Output

24

Input

code forces

Output

1574

Input

aaaaa aaa

Output

0

Input

justamassivetesttocheck howwellyouhandlemodulooperations

Output

667387032

Note

In the first example there are:

• 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10";
• 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101";
• 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010";
• 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010";
• 2 pairs of substrings "aaa" and "b", each with no valid merging sequences;
• 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010";

Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.

inputFormat

outputFormat

Output the answer modulo 998 244 353.

Input

The first line contains a string x (1 ≤ |x| ≤ 1000).

The second line contains a string y (1 ≤ |y| ≤ 1000).

Both strings consist only of lowercase Latin letters.

Output

Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353.

Examples

Input

aaa bb

Output

24

Input

code forces

Output

1574

Input

aaaaa aaa

Output

0

Input

justamassivetesttocheck howwellyouhandlemodulooperations

Output

667387032

Note

In the first example there are:

• 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10";
• 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101";
• 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010";
• 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010";
• 2 pairs of substrings "aaa" and "b", each with no valid merging sequences;
• 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010";

Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.

样例

code
forces

1574

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